PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact John Roe, Dmitri Burago.

Title:Curvature and the sign of the Euler characteristic
Seminar:Geometry Luncheon Seminar
Speaker:John Roe, Penn State
Abstract:
A conjecture variously attributed to Hopf or Chern says that the Euler characteristic of a compact 2n-dimensional, nonpositively curved manifold should have sign (-1)^n. In dimension 2 this follows from the classical Gauss-Bonnet theorem and in dimension 4 from Chern's generalization, but in dimensions 6 and up local computations do not suffice for the proof. I'll talk about the analytic methods that go back to the work of Atiyah and Dodziuk in the 1970s, and especially about Gromov's beautiful proof that the theorem is true for a negatively curved Kahler manifold.

Room Reservation Information

Room Number:MB114
Date:11 / 11 / 2009
Time:12:15pm - 01:15pm